Finite Group Databasebeta

← #11793099

Subgroups — #11793099

Order 1152.

565 conjugacy classes of subgroups.

The subgroup lattice has 469 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5517C211yesmaximal, characteristic, complemented
2#10592704C211yesmaximal, characteristic
3#10591232C211yesmaximal, characteristic
4C2×#63570C211yesmaximal, characteristic
5C3×#4531C211yesmaximal, characteristic, complemented
6#10589170C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#71842—31nomaximal
9#68714—31nomaximal
10C2×#3828C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#890—21no—
18C3×#888—21no—
19C3×#878—22no—
20C3×C4×Dic6—22no—
21#63632—22no—
22#63581—22no—
23#63570—21no—
24#63570—21no—
25C3×#533—31no—
26#5517D311yescharacteristic, complemented
27C2×#825—31no—
28#5006—31no—
29#5006—31no—
30#5005—31no—
31#5005—31no—
32#5005—61no—
33C2×#805—31no—
34C3×H(3,ℤ/4)—31no—
35#4559—31no—
36#4533—31no—
37#4532—31no—
38#4531D311yescharacteristic, complemented
39#4523—31no—
40C22×C32×C4C2311yescharacteristic
41C2×#638—21no—
42#3828—21no—
43#3828—21no—
44#3828—21no—
45#3828—21no—
46C2×C4⋊(C3⋊D3)Q811yescharacteristic, complemented
47C2×C4×C3⋊D3—21no—
48C2×#634Q811yescharacteristic, complemented
49C22×C3×Dic3—21no—
50C2×C3×Dic6—22no—
51C32×C4⋊C4—21no—
52C32×C22⋊C4—21no—
53C32×C42D412yes—
54#3748—21no—
55#3748—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×#217—21no—
58C3×#217D412yes—
59C3×C4⋊Dic3—22no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×Dic3⋊C4—22no—
63C3×Dic3⋊C4—22no—
64C3×C4×Dic3—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C3×#208—21no—
70C3×#208—21no—
71C2×C3×C3⋊C8—21no—
72#2031—91noSylow
73C2×#235—31no—
74C2×#235—31no—
75C2×#235—61no—
76C2×C3×M16—31no—
77C3×C4⋊Q8—61no—
78C3×#125—61no—
79C3×C22⋊Q8—62no—
80C3×C4×Q8—62no—
81C3×#117—21no—
82C3×#117—31no—
83C3×#117—31no—
84C3×#117C2×D311yescharacteristic
85C3×#117C2×D311yescharacteristic
86C2×C3×C42—31no—
87#926C2×D311yescharacteristic
88#926C2×D311yescharacteristic
89C2×C4×Dic3C2×D311yescharacteristic
90C2×#208—31no—
91C2×#208—31no—
92C2×#208—61no—
93C2×#208C2×D311yescharacteristic
94#890—21no—
95#888—21no—
96#878—22no—
97C4×Dic6—22no—
98#825—61no—
99#825—61no—
100#806—62no—
101#806—62no—
102#805—61no—
103#805—61no—
104#805—64no—
105#805—62no—
106#805—62no—
107C23×C32C2×D411yescharacteristic
108C22×C3⋊D3—21no—
109C2×C32×C4—22no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×Q811yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116#638—41no—
117#638—41no—
118C2×C3⋊Dic3—21no—
119C4⋊(C3⋊D3)—21no—
120C4⋊(C3⋊D3)—21no—
121C4×C3⋊D3—41no—
122C4×C3⋊D3—41no—
123#634—21no—
124#634—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—42no—
129C2×C3×Dic3—41no—
130C3×Dic6—44no—
131C3⋊(C3⋊C8)—41no—
132C3×C3⋊C8—41no—
133#533—31no—
134#421—91no—
135C2×#104—91no—
136#410—91no—
137#344—91no—
138#339—91no—
139H(3,ℤ/4)—31no—
140C2×C3×Q8—62no—
141C22×C3×C4—21no—
142C22×C3×C4—61no—
143C22×C3×C4C22×D311yescharacteristic
144C22×C3×C4C22×D311yescharacteristic
145C2×#67—61no—
146C2×#67—61no—
147C2×#67—121no—
148C22×Dic3—21no—
149#235—62no—
150#235—62no—
151#235—61no—
152#235—61no—
153#235—61no—
154#235—61no—
155#235—61no—
156#235—61no—
157#235—61no—
158#235—61no—
159#235—121no—
160#235—121no—
161C2×D12—31no—
162C2×D12—31no—
163C2×D12—61no—
164C2×C4×D3—61no—
165C2×C4×D3—61no—
166C2×C4×D3—121no—
167C2×Dic6—22no—
168C2×Dic6—31no—
169C2×Dic6—31no—
170C2×Dic6—61no—
171C3×M16—61no—
172C3×M16—61no—
173C2×C3×C8—61no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—41no—
177C3×C4⋊C4—62no—
178C3×C4⋊C4—62no—
179C3×C4⋊C4—62no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C22⋊C4—21no—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—32no—
185C3×C22⋊C4—41no—
186C3×C22⋊C4—61no—
187C3×C42—22no—
188C3×C42—31no—
189C3×C42—31no—
190C3×C42—61no—
191C3×C42—61no—
192C3×C42—61no—
193C3×C42D1212yes—
194C3×C42#6712yes—
195#217—21no—
196#217#6712yes—
197C4⋊Dic3—22no—
198C4⋊Dic3—21no—
199C4⋊Dic3—21no—
200Dic3⋊C4—22no—
201Dic3⋊C4—22no—
202C4×Dic3—21no—
203C4×Dic3—21no—
204C4×Dic3—21no—
205C4×Dic3#6711yescharacteristic
206C4×Dic3#6711yescharacteristic
207#208—21no—
208#208—21no—
209#208—62no—
210#208—61no—
211#208—61no—
212#208—61no—
213#208—61no—
214#208—121no—
215C2×C3⋊C8—21no—
216C2×C3⋊C8—61no—
217C2×C3⋊C8—61no—
218C2×C3⋊C8—121no—
219C22×C32—41no—
220C22×C32#12011yescharacteristic
221C22×C32C22⋊Q811yescharacteristic
222C22×C32#12411yescharacteristic
223C2×C3⋊D3—41no—
224C2×C3⋊D3—81no—
225C32×C4—42no—
226C32×C4C22⋊Q811yescharacteristic
227C32×C4C22⋊Q811yescharacteristic
228C32×C4#12411yescharacteristic
229C32×C4#12411yescharacteristic
230C3⋊Dic3—41no—
231C3×Dic3—22no—
232C3×Dic3—42no—
233C3×Dic3—41no—
234C3×Dic3—81no—
235C2×#41—91no—
236C2×M16—31no—
237C2×M16—91no—
238C4⋊Q8—61no—
239#125—61no—
240C22⋊Q8—62no—
241C4×Q8—62no—
242#117—31no—
243#117—31no—
244#117D3211yescharacteristic
245C2×C42—31no—
246#104—181no—
247#104—181no—
248#104—182no—
249#99—182no—
250C23×C3—21no—
251C23×C3D3×D411yescharacteristic
252C23×C3C2×#6711yescharacteristic
253C22×D3—61no—
254C22×D3—61no—
255C22×D3—121no—
256C3×Q8—124no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—42no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—62no—
269C2×C3×C4—122no—
270C2×C3×C4—121no—
271C2×C3×C4C2×D1211yescharacteristic
272C2×C3×C4#23511yescharacteristic
273C2×C3×C4#23511yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4#23711yescharacteristic
276C2×C3×C4D3×Q811yescharacteristic
277C2×C3×C4D3×Q811yescharacteristic
278C2×C3×C4#23911yescharacteristic
279C2×C3×C4#23911yescharacteristic
280C2×C3×C4#23911yescharacteristic
281C2×C3×C4C2×#6711yescharacteristic
282C2×C3×C4C2×#6711yescharacteristic
283#67—122no—
284#67—122no—
285#67—121no—
286#67—121no—
287#67—121no—
288#67—121no—
289C2×Dic3—21no—
290C2×Dic3—21no—
291C2×Dic3—22no—
292C2×Dic3—42no—
293C2×Dic3—41no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—121no—
297D12—62no—
298D12—61no—
299D12—61no—
300D12—61no—
301D12—61no—
302D12—121no—
303C4×D3—122no—
304C4×D3—122no—
305C4×D3—121no—
306C4×D3—121no—
307C4×D3—121no—
308C4×D3—121no—
309Dic6—44no—
310Dic6—62no—
311Dic6—61no—
312Dic6—61no—
313Dic6—61no—
314Dic6—61no—
315Dic6—121no—
316C3×C8—121no—
317C3⋊C8—41no—
318C3⋊C8—122no—
319C3⋊C8—121no—
320C3⋊C8—121no—
321C2×C32—21no—
322C2×C32—21no—
323C2×C32—21no—
324C2×C32#39311yescharacteristic
325C3⋊D3—81no—
326#41—181no—
327#41—181no—
328#41—181no—
329#41—181no—
330C2×Q8—62no—
331C2×Q8—91no—
332C2×D4—91no—
333C2×D4—181no—
334C22×C4—61no—
335C22×C4—181no—
336C22×C4C2×D3211yescharacteristic
337M16—61no—
338M16—61no—
339M16—181no—
340M16—181no—
341C2×C8—61no—
342C2×C8—181no—
343C4⋊C4—21no—
344C4⋊C4—62no—
345C4⋊C4—62no—
346C4⋊C4—62no—
347C4⋊C4—61no—
348C4⋊C4—61no—
349C22⋊C4—21no—
350C22⋊C4—32no—
351C22⋊C4—61no—
352C42—31no—
353C42—31no—
354C42—61no—
355C42—61no—
356C42—61no—
357C42#62612yes—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—41no—
362C22×C3—41no—
363C22×C3—81no—
364C22×C3#88211yescharacteristic
365C22×C3#88511yescharacteristic
366C22×C3#89611yescharacteristic
367C22×C3#94611yescharacteristic
368C22×C3#94711yescharacteristic
369C22×C3#95311yescharacteristic
370C2×D3—122no—
371C2×D3—121no—
372C2×D3—121no—
373C2×D3—242no—
374C2×D3—241no—
375C2×D3—241no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—42no—
381C3×C4—42no—
382C3×C4—62no—
383C3×C4—82no—
384C3×C4—121no—
385C3×C4—122no—
386C3×C4—241no—
387C3×C4#87511yescharacteristic
388C3×C4#88511yescharacteristic
389C3×C4#89611yescharacteristic
390C3×C4#89711yescharacteristic
391C3×C4#94611yescharacteristic
392C3×C4#94611yescharacteristic
393C3×C4#94711yescharacteristic
394C3×C4#94711yescharacteristic
395Dic3—22no—
396Dic3—42no—
397Dic3—41no—
398Dic3—81no—
399Dic3—122no—
400Dic3—121no—
401Dic3—121no—
402C32#203111yescharacteristic, complemented, Sylow
403C23—181no—
404C23D3×#6711yescharacteristic
405Q8—124no—
406Q8—181no—
407Q8—181no—
408D4—181no—
409D4—181no—
410D4—361no—
411D4—361no—
412C2×C4—22no—
413C2×C4—61no—
414C2×C4—61no—
415C2×C4—62no—
416C2×C4—122no—
417C2×C4—121no—
418C2×C4—181no—
419C2×C4—361no—
420C2×C4—361no—
421C2×C4#379611yescharacteristic
422C2×C4#379711yescharacteristic
423C2×C4#379911yescharacteristic
424C2×C4#379911yescharacteristic
425C2×C4C2×#62611yescharacteristic
426C2×C4D3×#6711yescharacteristic
427C8—121no—
428C8—361no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—41no—
437C2×C3—41no—
438C2×C3—41no—
439C2×C3#467311yescharacteristic
440C2×C3#523111yescharacteristic
441D3—242no—
442D3—241no—
443D3—241no—
444C22—41no—
445C22—361no—
446C22—721no—
447C22#6388811yescharacteristic
448C22#6390711yescharacteristic
449C22#6397711yescharacteristic
450C4—42no—
451C4—62no—
452C4—121no—
453C4—122no—
454C4—241no—
455C4—361no—
456C4#6386411yescharacteristic
457C4#6387111yescharacteristic
458C4#6388811yescharacteristic
459C4#6390711yescharacteristic
460C3—21no—
461C3#6871411yescharacteristic, complemented
462C3#7184211yescharacteristic, complemented
463C2—21no—
464C2—21no—
465C2—21no—
466C2—721no—
467C2#1059131011yescharacteristic
subgroupG/H
centerC4#63864
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#393
prime radicalC2×#3828C22
hypercenter#117D32
hypocenterC32#2031
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#5517C2semidirect
5. C3×#4531C2semidirect
6. #10589170C2semidirect
7. #10589161C2semidirect
26. #5517D3semidirect
38. #4531D3semidirect
46. C2×C4⋊(C3⋊D3)Q8semidirect
48. C2×#634Q8semidirect
402. C32#2031semidirect
461. C3#68714semidirect
462. C3#71842semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#55172
#105927042
#105912322
C2×#635702
C3×#45312
#105891702
#105891612
#718423
#687143